1. Field of the Invention
This invention relates to a method of computing belt tension distribution of a metal-pushing V-belt for CVTs (Continuously Variable Transmissions) to be mounted on a vehicle.
2. Description of the Related Art
The metal-pushing V-Belt is an essential part of CVTs. It transmits power from one pulley to another through the compressive contacts between its V-Block elements, while the two sets of flexible steel rings running through the V-blocks maintain belt tension. The friction and sliding between the B-blocks and the rings make it difficult to construct a computer model for the V-belt.
Many researchers introduced complex nonlinear equations to represent the power transmitting mechanisms of CVTs like G.Gerbert, xe2x80x9cMetal V-Belt Mechanicsxe2x80x9d, ASME paper, 84-DET-227, pp. 9, 1984; H.Kim et al, xe2x80x9cAnalysis of Belt Behavior and Slip Characteristics for a Metal V-Belt CVTxe2x80x9d, MPT91 Proc. Of JSME Int. Conf. On Motion and Power Transmission, Vol. 62, pp. 394-399, 1991; D. C. Sun, xe2x80x9cPerformance Analysis of Variable Speed-Ratio V-Belt Drivexe2x80x9d, J. Mech. Transmission. Autom. Design Transactions of the ASME, Vol. 110, pp. 472-481, 1988; J. M. Carvajal et al., xe2x80x9cC.V.T Transmission Analysis; A Mechanical Discrete Analysis with Computerxe2x80x9d, I.N.S.A-Bar-113; and D.Play et al., xe2x80x9cA Discrete Analysis of Metal V-Belt Drivexe2x80x9d, ASME Int. Power Transmission and Gearing Conf., DE-Vol. 43-1. They simplified the CVT system by assuming no radial motion of the V-blocks relative to the pulleys.
Y.Fushimi et al., xe2x80x9cA Numerical Approach to Analyze the Power Transmission Mechanisms of a Metal Pushing V-Belt Type CVTxe2x80x9d, SAE Paper 960720, 1996, borrowed R. Kido""s quasi-static approach (mentioned in xe2x80x9cA New Approach for Analyzing Load Distribution of Toothed Belts at Steady Sates Using FEMxe2x80x9d, SAE Paper 940690, 1994) to obtain a steady-state solution of the CVT model. They modeled the metalxe2x80x94pushing V-belt using linear springs and interface (contact) elements. The linear springs are defined between the blocks, between the rings, between the blocks and pulleys. The interface elements are defined between the blocks and pulleys and between the blocks and rings. They modeled half of the CVT system, assuming that the system is axially symmetric.
S. Kuwabara et al., xe2x80x9cPower Transmission Mechanisms of CVT Using a Metal V-Belt and Load Distribution in the Steel Ringxe2x80x9d, SAE Paper 980824, 1998 proposed a numerical model that allows minute rotations of both driving and driven pulleys so that the rings could influence the overall dynamics of the CVT system. H. Shimizu et al (xe2x80x9cDevelopment of 3-D Simulation for Analyzing the Dynamic Behavior of a Metal Pushing V-Belt for CVTsxe2x80x9d, JSAE Paper, Vol. 8-99, 1999) developed a 3-dimensional CVT model based on a commercial FEM simulation program. They modeled each block and band as separate finite-element bodies. Their simulation results showed good quantitative agreement with the experimental data. However, the computational cost was very high with about 50 hours by CRAY T90 super computer.
Furthermore, Kanehara et al. propose measuring compression force between the blocks and ring tension using a micro load cell installed on the blocks in xe2x80x9cA Study of a Metal Pushing V-Belt Type CVT; Part 2: Compression Force Between Metal Blocks and Ring Tensionxe2x80x9d, SAE Paper 930667, 1993. This needs to machine the blocks to install the small sensor thereat and is tedious. In addition, this configuration will make accurate measurement difficult at high speed, since the high speed rotation could damage the sensor and affect measuring devices connected to the sensor.
An object of this invention is to provide a method of computing belt tension distribution of a metal-pushing V-belt for CVTs, by modeling the metal-pushing type V-belt assembly. The blocks are modeled as rigid bodies with number of discrete contact points to represent any surface to surface contact between adjacent blocks and between a block and a pulley. It has been known that friction forces between the rings (laminated steel bands) and the blocks (V-shaped steel elements) induce a non-uniform ring tension distribution along the V-belt, which in turn affects the block-to-block compression force distribution along the belt. Complex nature of the ring in its elastic deformation and in the distributed contact and friction with many blocks makes it not practical to model the ring as a chain or rigid bodies or as a finite element-based elastic body. In order to circumvent this problem, the ring is modeled as a virtual element that exists only as the second order differential equation but still retains its elasticity, overall shape, and tension distribution. It is assumed that a ring is composed of one steel band and that the ring tension is applied to the left and right saddle surface centers of each block. The virtual ring concept relies upon the instant locations and orientations of the blocks to compute the total length, local bending, block-to-ring friction distribution, and tension distribution of the ring. The total ring length determines the pure elastic ring tension. The block-to-ring friction distribution along the ring provides the basis for computing the final tension distribution of the ring. Simulation results show a good agreement with experimental results both in ring tension distribution and block compression distribution along the belt.
In order to achieve the object, the present invention provides a method of computing belt tension distribution of a metal-pushing V-belt for CVTs having an array of V-shaped blocks and a plural sets of rings each running through slots formed at the blocks and wound around pulleys; comprising the steps of: modeling the blocks as rigid bodies with contact points to represent surface to surface contact between adjacent blocks and between the blocks and the pulleys, while modeling the rings as a closed-loop string which is subject to an elastic tension caused by the pulleys; dividing the closed-loop string into string segments, and computing the elastic tension and computing a friction force caused by at least one of the blocks for each of the string segments using the computed elastic tension as an initial value; computing a friction-induced-tension based on the computed friction force for each of the string segments; computing an average of the computed friction-induced tensions of the string segments; repeating the steps (b) to (d) until the average converges to the tolerance value; and computing a ring tension based on the average to determine the belt tension distribution based on the computed ring tension.